d20 to 3d6 Gaming

[SolkaTruesilver]

Hi there, I love bell curves, and I find them much more appropriate for a "reality simulator" than the flat distribution offered by the d20.

I wanted to know if any of you ever tried to change the regular d20 for all checks (attack roll, skill, caster roll) for a 3d6?

I though giving the values 18-17 the "critical hit" and 3-4 the "critical miss", but I still wonder how to convert the 19-20 value, let alone the 18-20, the 17-20 and the 15-20?

[Kurald Galain]

Read up on GURPS; it uses a 3d6 curve.

You can easily calculate the odds for 3d6 to come up on, say, 16+.

[Starsinger]

http://www.d20srd.org/srd/variant/adventuring/bellCurveRolls.htm There you go, the rules for playing D&D with a bell curve instead of a d20.

[Rad]

I played GURPS and trust me, 3d6 is too steep a curve. It might be ebtter with d20 which also has the DC to move the bell around, but with GURPS you can really feel the problems when you hit high skill scores.

[Yakk]

In effect, the "scale" of each +1 modifier is much larger under 3d6 than under d20.

You can measure the scale of modifiers in a RNG via what is known as the variance.

The variance of each die is (k)(k+2)/12. Variance adds up linearly.

So Variance(d20) =~ 36.67
Variance(d6) = 4
Variance(3d6) = 3*Variance(d6) = 12

Next, take the square root to go from Variance to Standard Deviation.

SD(1d20) =~ 6.06
SD(3d6) =~ 3.46

The SD of 3d6 being about 1/2 that of 1d20 means that each +1 modifier is roughly twice as important under 3d6 as under 1d20.

This has a significant impact on game balance -- among other things, the level curve just got a lot steeper, and attribute modifiers now matter a lot more.

If you want something "curvy", try rolling 1d20 for attack and 1d20 for defense. This works out to roughly 2d20, and a SD of about 8.56. Under this option, each +1 modifier to your rolls is worth about 2/3 as much as the standard D&D game.

You can also go all the way to 3d6 minus 3d6 -- both sides roll 3d6.

That gives you a total variance of 24, and a SD of 4.90 -- 80% of the SD of standard d20. (Ie, +modifiers to d20 rolls are roughly 25% more important than under standard d20).

That will have less problems than just rolling 3d6 for each action.

...

Crits are a bit tricky, but on the plus side core D&D crits are rather broken. :)

[Kurald Galain]

In effect, the "scale" of each +1 modifier is much larger under 3d6 than under d20.


I would consider that a good thing, because a +1 modifier on 1d20 really doesn't amount to all that much.

The "+2 circumstance bonus" rule is very nice and all that, but in practice it is irrelevant far too often.

[Reinboom]

2d10 could work for a bell curve without curving too much.
Not quite as significant an impact as 3d6, leaves 20s in tact and less rules modifying. (1 becomes 2, not that big of a change)

Just.. note that how weapon crits are set up is going to be further stretched, and larger crit ranges will become a lot more significant than a higher crit multiplier.

[Yakk]

So an example.

Someone wearing full plate and a large shield being attacked by a level 1 warrior with 14 strength.

AC: 20
Warrior AB: +3

Standard D&D: 15% chance to hit (17+)
3d6 D&D: 1.85% chance to hit (17+)

A level 20 warrior with 28 strength and a +5 weapon, and +1 other bonus to hit, is attacking (+35 to hit).

Also attacking is a level 20 rogue with 28 dex and a +5 weapon, and a +1 other bonus to hit (+30 to hit).

The target has an AC of 43.

Standard D&D:
Warrior has 65%/40%/15%/5% chance to hit. 1.25 hits on average
Rogue has 40%/15%/5% chance to hit. 0.6 hits on average

3d6 D&D:
Warrior has 84%/26%/0.5%/0.5% chance to hit. 1.11 hits on average.
Rogue has 26%/0.5%/0.5% chance to hit. 0.27 hits on average.

Notice how the Rogue got reamed.

...

Now, you can patch over these things. But you have to be extra careful about the impact of modifiers on d20 rolls, or the game goes off the rails.

First step: Reduce starting attributes.
Second step: Reduce the number of bonuses you can get to hit/damage.
Third step: Reduce skill bonuses from high quality tools and the like.
Forth step: Provide a way for 3/4 BaB classes to get full BaB at some cost.

Ie, for the two core 3/4 BaB meleers:
Rogues get +1 to hit during a sneak attack at level 1, 5, 9, 13, and 17 (rogue level/4, rounded up).

Monks who full attack take no penalty on their flurry.

Monks who simple attack can flurry for -2 to hit.

Against a target the monk hasn't hit, the monk gains a bonus to hit of level/4, rounded up.

Monks may use their "fast move" during a full attack instead of a 5' step as a kind of "bonus move action".

...

There, now both Rogues and Monks can do their job without being gimped due to the d20 roll modifiers.

Rangers who TWF also need some help, because those -2 penalties are worse under 3d6.

Etc etc.

[Frosty]

I'm thinking of experimenting with a 2d10 system as well with a few minor midifications. For example, if both of your dice rolls are 1s, you critically fail. This is much harder to do than the current auto-failure on a roll of a 1 on a 1d20. This would also mean criticals happen less frequently.

[pasko77]

About critical hits:

The critical on 20 should become on 16+, to keep the same probability.
The critical on 19+ should become on 15+ and so on, but the odds would slightly differ.
Or, you might want them to change, but in this case you'll have to rewrite rules for critical multipliers.

Edit:
oops. This is already said in the link given above.

[Kizara]

My homebrew on the matter:

The 2d10 Variant:

-Whenever you would normally roll a d20 for task-resolution purposes, instead roll 2d10. -If you get a result of 20, roll a d20 to confirm your critical normally.
-If you get a result of 2, roll a d20 to confirm your critical failure. If your roll fails to make the DC required for success, you critically fail.
-If you roll a 1 on a critical failure confirmation, you catastrophically fail and your DM is encouraged to invent an extremely bad result of your attempted action. For instance, if you catastrophically fail an attack roll, you could instead roll to attack your ally, who would be denied his Dex bonus to AC against your attack, and the resulting confusion would cause you both to provoke an Attack-of-Opportunity.
-Any reference to consequences to “rolling a 1” on a d20 instead refer to “confirming a critical failure”.

-If you use this variant, you will also want to change the critical values on weapons as follows:

20/x2 -> 20/x3.5 (calculate as if x4, but deal only half damage on the final ‘hit’)
19-20/x2 -> 19-20/x3
18-20/x2-> 18-20/x2
20/x3 -> 20/x5
20/x4 -> 20/x6

-Criticals now are significantly nastier, but also have drastically less likelihood of occurring.
-Factors such as keen or Improved Critical still work as-written.
-Critical-dependant abilities such as Flamming Burst deal more damage as indicated by the increased critical multiplier.
-Vorpal now is only +4 market price modifier.

[Yakk]

Variance(2d10) = 2*Variance(1d10) = 2*10 = 20
SD(2d10) = sqrt(Variance(2d10)) =~ 4.47

Chart:
SD(d20vd20) =~ 8.57
SD(2d10v2d10) =~ 6.32
SD(1d20) =~ 6.06
SD(3d6v3d6) =~ 4.90
SD(2d10) =~ 4.47
SD(3d6) =~ 3.46

Or, using SD(1d20) as a baseline, we get:
1d20 V 1d20: 71%
2d10 V 2d10: 96%
1d20 V fixed: 100%
3d6 V 3d6: 124%
2d10 V fixed: 136%
3d6 V fixed: 175%

Those are the "scaling factors" that each RNG applies to each +1 or -1 modifier on a "d20" check.

So note you can create a very similar effect to "3d6 V fixed" by simply doubling all modifiers to d20 rolls.

[Frosty]

Variance(2d10) = 2*Variance(1d10) = 2*10 = 20
SD(2d10) = sqrt(Variance(2d10)) =~ 4.47

Chart:
SD(d20vd20) =~ 8.57
SD(2d10v2d10) =~ 6.32
SD(1d20) =~ 6.06
SD(3d6v3d6) =~ 4.90
SD(2d10) =~ 4.47
SD(3d6) =~ 3.46

Or, using SD(1d20) as a baseline, we get:
1d20 V 1d20: 71%
2d10 V 2d10: 96%
1d20 V fixed: 100%
3d6 V 3d6: 124%
2d10 V fixed: 136%
3d6 V fixed: 175%

Those are the "scaling factors" that each RNG applies to each +1 or -1 modifier on a "d20" check.

So note you can create a very similar effect to "3d6 V fixed" by simply doubling all modifiers to d20 rolls.

What do these things mean? What's 2d10 V 2d20? What's 2d10 V fixed?

[Yakk]

1d20 V fixed:
Roll 1d20+5 attack bonus vs 20 AC
1d20 V 1d20:
Roll 1d20+5 attack bonus vs 1d20+10 AC bonus.

2d10 V fixed:
Roll 2d10+5 attack bonus vs 20 AC.
2d10 V 2d10
Roll 2d10+5 attack bonus vs 2d10+10 AC bonus

Ie: 1d20 V fixed means that your target numbers are fixed.
1d20 V 1d20 means that your target numbers are also rolled.

With both sides rolling, you get an increase in the amount of randomness, and thus a decrease in the amount that each +1 modifier matters.

The percentages are scaling factors.

Take 1d20 V 1d20: 71%.

Suppose we had:
1d20+10 vs 1d20+15
That is roughly the same as:
1d20+7 vs DC 10+(15*.71) = DC 20

In a sense, almost all of the effect of "rolling more dice" is just a matter of rescaling the size of the modifiers to your DC and your roll.

Or, similarly:
3d6+4 vs 10 AC
is very similar to
1d20+4*1.75 = 1d20+7 vs 10 AC

There are extra effects from the bell curve of rolling 3d6, but they are smaller than the effects of the "modifier rescale". If you graph the chance of beating a target with a given "edge" compared to you, and rescale by the percentages I posted, the graphs end up looking very close to each other.

There are slight differences, but they are smaller than you'd think, near the middle. There are also differences at the "tails", but in general those tails tend to sum to a small percentage of events.

So, as mentioned: the largest effect of changing what dice you roll is that they effectively rescale the importance of modifiers to your rolls. A rough indicator of how the modifiers are rescaled is listed in my previous post.

Values less than 100% mean that under that system, modifiers are less important than the standard d20 system.

Values more than 100% mean that under that system, modifiers are more important than the standard d20 system.

In either case you have to take care. If you make modifiers more important, effective "auto hit" becomes more common, as does "auto miss". If you make them less important, then classes whose advantage is things like "higher BaB" end up with more problems, as their bonus is shrunk.

[Frosty]

Since I want to reduce randomness a bit, 2d10 would be a good thing. I really think critical fumbles happen way too often. So in a 2d10 system, modifiers become 36% more important. I like that. A heroic level 20 fighter should not miss against Joe Schmoe the Fat with a DEX of 6 about 5% of the time. I can see one out of every 100 swings missing due to bad luck, but that's about it.

[Kizara]

Since I want to reduce randomness a bit, 2d10 would be a good thing. I really think critical fumbles happen way too often. So in a 2d10 system, modifiers become 36% more important. I like that. A heroic level 20 fighter should not miss against Joe Schmoe the Fat with a DEX of 6 about 5% of the time. I can see one out of every 100 swings missing due to bad luck, but that's about it.

What do you think of my take on the matter?

[Frosty]

Kizara: I'd most likely be doing something like that, except I'd probably keep the critical nastiness as they are, and raise the threat-range instead to compensate. Maybe increase threat range by 2 for all weapons. And then I'll have to change the way Improved Critical works.

[Voyager_I]

I like it, except for the "Vicious and Arbitrary Critical-Critical-Failures". Randomness still hurts PC's, and having critical misses screw them over by however much the DM feels like just increases the chances that they will get completely shafted in the middle of a key battle through no fault of their own and with no way of avoiding it. Just because it doesn't happen often doesn't mean that the PC's should be absolutely screwed if it does. I feel the same with the "Three twenties in a Row equals INSTANT KILL!!!" rules, personally. If it's something that comes up once in every several hundred attacks, the PC's aren't going to expect to do it, they aren't going to be planning based on the assumption it will happen, and they shouldn't have to worry about losing fights or characters because of it.

[Kizara]

Ok, you need to realize a couple things in order to understand my system:

1) It is designed to and suceeds at drastically reducing the element of luck in the game and generally favors PCs.

2) The normal chance for a critical failure is 5% or 1 in 20. The chance for a critical failure under my system (assuming you fail on a 6 or less) is something like 1/135. The chance for a catastrophic failure is 1/2000. That's right, 1 in two thousand. Personally, I feel that something that rare has a bit of a right to be dramatic.

3) You still are much less likely to lose fights and characters with this system compared to the normal one: Monsters have a harder time criticaling you, and only do a bit more damage if they do. You are much more likely to hit with your attacks.

Also, this system indirectly benefits non-spellcasters because its easier to get an average roll so you can hit consistantly, but its less likely to roll poorly on a save to fail to a save-or-suck effect.

[Chronos]

You can measure the scale of modifiers in a RNG via what is known as the variance.

The variance of each die is (k)(k+2)/12. Variance adds up linearly.Are you sure about that formula? When I worked it out a while back, I found variance = (k^2 - 1)/12 . Which agrees asymptotically for large dice, of course, but differs significantly for small dice. In the extreme case, your formula would give a variance of 1/4 (and hence standard deviation of 1/2) for a d1, while my formula gives the correct value of 0.


Standard D&D:
Warrior has 65%/40%/15%/5% chance to hit. 1.25 hits on average
Rogue has 40%/15%/5% chance to hit. 0.6 hits on average

3d6 D&D:
Warrior has 84%/26%/0.5%/0.5% chance to hit. 1.11 hits on average.
Rogue has 26%/0.5%/0.5% chance to hit. 0.27 hits on average.

Notice how the Rogue got reamed.I don't see the rogue getting reamed there. What I see is the rogue and fighter both getting more specialized. Under a 3d6 system, the fighter is significantly better in combat than the rogue, and that's as it should be, since combat is supposed to be what the fighter has dedicated his training to. Meanwhile, though, if we make the comparison between the rogue and fighter's skills (say, Move Silently vs. Listen), we'll find that the rogue is now significantly better at sneaking than the fighter. Which also makes sense, since that's what the rogue is spending all his time on.

[Voyager_I]

2) The normal chance for a critical failure is 5% or 1 in 20. The chance for a critical failure under my system (assuming you fail on a 6 or less) is something like 1/135. The chance for a catastrophic failure is 1/2000. That's right, 1 in two thousand. Personally, I feel that something that rare has a bit of a right to be dramatic.

I understand. It's just my belief that if something has such an infinitesimally small chance of happening that the PC's are expected to plan as if it will never happen, it just shouldn't happen. Remember, randomness favors monsters; they're not expected to survive the encounter, whereas the PC's entire campaign can be ruined by one bad roll and a vicious rule.

I don't like the rule because it will happen so rarely that it can pretty much be assumed it won't happen, not even once. However, over the course of an entire campaign, there actually is a reasonable chance of it happening, and that can basically be a random "Game Over" that the PC's have no control over and no ability to predict.

Considering you're trying to reduce randomness, it seems rather counterintuitive to add in a "By the way, there's a very, very small chance that you're all going to be screwed" clause.

[SolkaTruesilver]

I don't see the rogue getting reamed there. What I see is the rogue and fighter both getting more specialized. Under a 3d6 system, the fighter is significantly better in combat than the rogue, and that's as it should be, since combat is supposed to be what the fighter has dedicated his training to. Meanwhile, though, if we make the comparison between the rogue and fighter's skills (say, Move Silently vs. Listen), we'll find that the rogue is now significantly better at sneaking than the fighter. Which also makes sense, since that's what the rogue is spending all his time on.

On the other hand, the Fighter both get screwed when pitted against the Barbarians, since the +4 Str (up to +8) REALLY changes matters.

on the other hand, Tower shield immediatly becomes REALLY badass.

[Tsotha-lanti]

I played GURPS and trust me, 3d6 is too steep a curve. It might be ebtter with d20 which also has the DC to move the bell around, but with GURPS you can really feel the problems when you hit high skill scores.

What problem? That high skills make you better at difficult tasks?

I find the system excellent - difficulty modifiers scale well. A skill 20 character is as likely to succeed at a routine task as a skill 16 character, but way more likely to succeed at a difficult -6 modifier task.

Using combat skills as an example, the skill 16 fighter can hit you all the time (in ideal circumstances), but the skill 20 fighter can hit your heart all the time.

For combat skills, specifically, parry/block continues to scale, and the closer you get to 10/11, the bigger each step of 1 is (the difference in %-chance of success between 5 and 6 is small, but the difference between 9 and 10 is big).

I find this somewhat superior to D&D's (and many other games') "roll+modifier VS target number" system, although both are much superior to "roll under skill, possibly modified up or down" systems.

In BRP, for instance (where skills are expressed as a percentage chance of success), a -40% modifier to the skill (to represent a difficult task) will make the task impossible for low skills (except for the 5% chance of automatic success) of 45% or below. Similarly, a +40% modifier (to represent an easy task) will mean there's no chance of failure (except the 5% chance of automatic failure) for someone of skil 55% or above).

It kinda sucks, because difficult tasks aren't "you may fail!" but rather "you must be this tall to try!"

[warmachine]

Yakk analyses the idea well and is ample evidence why it's a bad idea. I'll just add that d20 is built around the assumption flat dice distribution whereas GURPS is built around the bell curve. Changing a fundamental, system-wide aspect of any design usually breaks it and patches results in horrible, painful quirks everywhere. A complete redesign usually saves a lot of pain in the long run.

[Tsotha-lanti]

Yakk analyses the idea well and is ample evidence why it's a bad idea. I'll just add that d20 is built around the assumption flat dice distribution whereas GURPS is built around the bell curve. Changing a fundamental, system-wide aspect of any design usually breaks it and patches results in horrible, painful quirks everywhere. A complete redesign usually saves a lot of pain in the long run.

This is absolutely true. The success chances don't translate at all. The DC system - and especially the standard DCs - would get wrecked entirely. You'd have to rework everything, slow down AC and save/skill/check DC progressions, etc.

[Jack Zander]

Why don't you try rolling 3d20 and take the median (the middle value of the three)?

[only1doug]

Why don't you try rolling 3d20 and take the median (the middle value of the three)?

this still breaks weapons with a crit range of other than 20. the design of crit ranges on weapons was to make the weapon twice (19-20) or three times (18-20) as likely to crit and keen will double that to four times (17-20) or six times (15-20) as likely. taking the most broken case 15-20 is far more than six times as likely to be the median number of 3d20 than 20 is.

adding patches in to even out such discrepencies when you figure them out is a big hassle and ultimately harder work than just changing to a system that was designed for bell curve results in the first place.

[Zeta Kai]

Kizara, for the record, I like your system. I prefer 2d10 to 3d6, as the curve is not as steep. I was thinking about drafting up a 2d10 variant in Homebrew before I saw your system. Good job.

[Greenfaun]

I first want to say that I know I don't completely understand the math, but since we've got a couple people busting out real statistics and whatnot, maybe this is the place to ask:

Isn't a bellcurve counterproductive in the D20 system, which uses the roll to determine straight success or failure? I mean, rolling a 16 isn't any better than rolling a 2 if neither one beats the DC. All the D20 does is provide randomness in 5% slices, right? The D20 is like flipping a coin between success and failure, you just have more choices between the relative probabilities. Other than success, rolling high doesn't help, and other than failure, rolling low doesn't hurt.

The whole crit roll adds a little complexity, but is there any mechanical difference between "On a 20, roll to confirm and do double damage" and "On a 20, get a free extra attack at the same bonus"? Now, it gets weird when the only way to even hit a creature is to threaten a crit, but that's the edge case, and even so it's internally consistent, if counterintuitive.

My point is, wouldn't bell curves be better suited to a game with a range of outcomes based on the actual value of the roll? Maybe beating the AC by 10 is a crit, by 5 is a little extra damage, by less than 5 is just a hit, then under by more than 5 is a fumble, more than 10 is an opening for an opportunity attack, etc. I'm not saying that's the way to do it, just for an example. In this scheme, you expect to stay in the middle range between +5 and -5 most of the time if you're facing appropriate challenges, but the occasional outlier rolls are still frequent enough to make things interesting.

Also, to shift gears, I once had the thought of using 2d10 both for bell-curviness and to add a bit of narrative play into the standard dicerolling. My scheme was:

double-10 (1/100): Automatic critical success
other double (8/100): positive narrative event
Double-1 (1/100)Automatic critical failure

The narrative events would help whoever rolled the double, suggested by the players but approved and adjudicated by the GM. No major bonuses, just plot twists, coincidences, or stunts to spice up the combat descriptions or add a wrinkle to the plot without hurting balance too much. That way, the odds are shifted towards the middle, bonuses matter more, but one in ten rolls still results in something cool happening. I confess I lost interest when I realized I didn't like any of my options for handling crits though.

[Tsotha-lanti]

My point is, wouldn't bell curves be better suited to a game with a range of outcomes based on the actual value of the roll?

I think that adequately sums up most of the posts in this thread, yes.